Abstract In the last decade, computer-generated images have become a vital and integral part of our everyday lives. The quality of these images depends considerably on the geometric representation of the underlying virtual 3D environments. Subdivision surfaces, one such representation, have been found to be very useful due to their unique geometric properties. These properties led to the adaptation of subdivision surfaces as a movie industry standard for modeling 3D geometry, making subdivision surfaces indispensable in today's film productions. However, despite the high surface quality of subdivision surfaces, the complexity of underlying calculations requires a significant computational budget. In this thesis, we address this problem and propose novel algorithms to accelerate the evaluation of subdivision surfaces by several orders of magnitude. This enables the rendering of high-quality movie content on commercially available desktop computers within only a few milliseconds, opening up the possibility of using subdivision surfaces in real-time applications (e. g., video games). The results of this work have been made publicly available in Pixar's open source initiative OpenSubdiv, which is used in many industry applications (e. g., Maya, a modeling software by the industry leader Autodesk). Our algorithms can also be found in video games such as Activision's best seller Call of Duty: Ghosts, where we now can enjoy the surface quality of movies.